What Causes the Upward Force Counteracting Gravity?

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The upward force counteracting gravity, known as the normal reaction force, arises from the repulsion between atoms in a surface when weight compresses them. This force is often overlooked in physics classes, where it is treated merely as a bookkeeping exercise for balancing forces. The discussion highlights that pressure must be equal in all directions within a fluid at rest, leading to the conclusion that horizontal and vertical pressures are equivalent. An analogy with oiled ball bearings illustrates that the force exerted by a fluid is consistent regardless of the direction of the pressure. The conversation also seeks a mathematical demonstration of equal pressure in fluids, similar to the ideal gas law for gases.
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I know that gravity causes the downward force, but to keep us in ballance there is an upward force.Can someone tell me what causes this upward force.
 
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normal reaction force
 
Your weight is trying to push the atoms in the floor closer together, the electrical charges in the atoms repel each other and push back.

Strangley most phyiscs classes don't seem to mention this - the reaction force is treated as just a book keeping exercise to make all the forces balance.
 
mgb_phys said:
Your weight is trying to push the atoms in the floor closer together, the electrical charges in the atoms repel each other and push back.

Strangley most phyiscs classes don't seem to mention this - the reaction force is treated as just a book keeping exercise to make all the forces balance.

I get this, but I don't understand why the pressure must be the same in every direction. If you take a small cube in a fluid at rest, the net force must be zero. So pressure must be equal on opposite sites. But why does this mean that the horizontal pressure must equal to vertical pressure?
 
That's a slightly different question - but yes.
It's difficult to immediately see why the force on the walls of the bottom of a tank of water is the same as the force on the base.
Imagine something heavy that can easily flow, like oiled ball bearings.
Now picture a large box full of them and you cut a hole in the side - you would need a lot of force to hold back the balls. The force of them coming out of a hole in the side, near the bottom, is pretty much the same as the force of them coming out of the bottom - there is still the same weight of all the balls on top of them.

The same thing applies to water or air, or any other fluid - the pressure acts in all directions because the particles are being pushed out in all directions by the weight of the fluid above them
 
I see, thank you!
 
Speaking of pressure, is there a way to show a fluid exerts equal pressure in all directions mathematically? Like for ideal gases we can use the assumption that collisions with the walls of the container are perfectly elastic to show that pV =1/3Nm<v^2> where <v^2> is the mean square speed of the particles.

Is there some other mathematics for a fluid as well?
 

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